Elementary number theory
Elementary number theory [ edit ] The term elementary generally denotes a method that does not use complex analysis . For example, the prime number theorem was first proven using complex analysis in 1896, but an elementary proof was found only in 1949 by Erdős and Selberg . [77] The term is somewhat ambiguous: for example, proofs based on complex Tauberian theorems (for example, Wiener–Ikehara ) are often seen as quite enlightening but not elementary, in spite of using Fourier analysis , rather than complex analysis as such. Here as elsewhere, an elementary proof may be longer and more difficult for most readers than a non-elementary one. Number theorists Paul Erdős and Terence Tao in 1985, when Erdős was 72 and Tao was 10. Number theory has the reputation of being a field many of whose results can be stated to the layperson. At the same time, the proofs of these resu...